I had a toy hauler that we carried a TJ in. Before I bought it I called the factory and asked about hauling the Jeep. They said the weight was fine but I needed to beef up the floor. After running the numbers I decided to use 3/16's inch diamond plate on the floor that ran the length of where the jeep parked. Then I went to the next size up axles because my wife liked to load every compartment. If you need to stiffen the frame, I would bridge it with flat stock at least 1/4 inch thick the same width as the frame. Then use round tube in varying length to make an inverted truss under the frame. Any good shop could do it if it is above your welding/time capabilities. I hope this helps. Your only other option is to get a Motorhome and a trailer. The door may need some beef also. Use Aluminum channel for the door.

X2
We looked at doing the same thing. Chances are the tires will end up in between the floor joists and with the constant bouncing the rig will do.........the tires will blow through the floor.